Problem: Simplify the following expression: $\sqrt{176} + \sqrt{99}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{176} + \sqrt{99}$ $= \sqrt{16 \cdot 11} + \sqrt{9 \cdot 11}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{11} + \sqrt{9} \cdot \sqrt{11}$ $= 4\sqrt{11} + 3\sqrt{11}$ Finally, simplify by combining the terms. $= ( 4 + 3 )\sqrt{11} = 7\sqrt{11}$